RETRACTED: The increased viscosity effect for fracturing fluid imbibition in shale formation (Retracted article. See vol. 208, 2022)

Understanding water imbibition behaviors in shale formations plays an essential role in shale gas development and risk assessment on shallow aquifer contamination, as imbibition is the main mechanism for fracturing fluid uptake during a hydraulic fracturing stimulation process. The effective viscosity of water in shale formations is usually different from that of the bulk phase due to confined conditions. In this work, a model considering interactions between water and a solid surface is proposed to predict the effective viscosity of water at the nanoscale. This model is derived based on a classical molecular kinetic theory and incorporates the disjoining pressure. Published experimental data is used to validate the model. It is demonstrated that the effective viscosity of water highly confined in hydrophilic nanopores is much higher than that of the bulk phase, while that in hydmpholic nanopores is less than the bulk phase value. Furthermore, geometric factors, including the characteristic length of pores and the pore shape, significantly affect the effective viscosity. Moreover, it is found that for the pores in the shale formation which are open for imbibition, the proposed model can be applied as the extremely small pores are usually filled with initial water. This work establishes a theoretical foundation to understand fracturing fluid imbibition behavior in shale gas reservoirs, which will benefit the simulation of fluid flow within shale formations at the reservoir scale.